Waheed Borsh was convicted of "rendering services to an illegal organisation without intention", his lawyer Lea Tsemel told AFP.
The Israeli justice ministry confirmed the plea deal, saying that it also included eight months' probation.
Borsh was arrested in July and with time already served and good behaviour, he is expected to be released on January 12.
The case centred on accusations that rubble in Gaza under the responsibility of the United Nations Development Programme (UNDP) was misused by the militant group Hamas that controls the enclave.
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Israel originally alleged that Borsh had been recruited by Hamas, which is considered a terrorist organisation by the European Union, the United States and Israel, and had deliberately diverted rubble to a port -- which was then used to build a military jetty.
But Tsemel stressed that her client had been convicted only of unintentionally aiding the Islamists for "moving some rubble".
"The prosecution claimed that he should have checked better as this could have helped Hamas."
There were was no immediate comment from the UNDP.
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